How many ordered pairs (a, b) of positive integers satisfy the equation

a \cdot b+63=20 \cdot \operatorname{lcm}(a, b)+12 \cdot \operatorname{gcd}(a, b)

where \operatorname{gcd}(a, b) denotes the greatest common divisor of a and b, and \operatorname{lcm}(a, b) denotes their least common multiple?

**Answer Choices**

A. 0

B. 2

C. 4

D. 6

E. 8